We're gonna have to disagree out the gate. A manifold has a precise definition as a surface which is locally Reimanian, something like that. I'd classify it as one of the more elaborate constructs, and less primitive or whatever than a simple set. Afterall, you need set elements to talk about before you can define a manifold. All the formal stuff I've seen looks like "a group is a SET, with the following additional properties...".
Reading the rest I do see how you mean though, so I'll stop getting hung up on technical definitions. Yeah, I'd think patterns or differences come first, then the notion of distinct things. That's how I'm roughly understanding you.
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i guess the thing i'm disagreeing on relates to a definition of a surface that requires discrete or compositional elements to describe.
a point is before a set, a set is a collection of points. a line can be divided, then you can make a set, a set could be said to be all sets of points in a single dimension. you can make that dimension infinite, or you can make it circular, again, the geometry precedes the establishment of a set.
a point is the primary unit of topology. so i guess i'm splitting hairs.
i just don't agree with the post-hoc nature of sets, being primordial compared to the ad-hoc nature of divisions of surfaces.
and yes, that's the thing, you have to have a thing before you can talk about a thing.
